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I was discussing with a colleague the use of modern dispersion-corrected density functionals. I take it almost as a given that the methods generally produce "better" (for some definition) geometries, in addition to more accurate predictions of thermodynamic and other properties.

Naturally, since the dispersion correction involves intermolecular interactions (e.g., van der Waals complexes), they should do better than "regular" functionals. I'm curious about intramolecular geometries.

Are there any benchmark comparisons on bond lengths, angles, etc. comparing different computational methods (DFT and otherwise) to crystal structure or other geometries?

In other words, how accurate are different computational methods at getting geometric properties of individual molecules?

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  • $\begingroup$ I remember that I did my own very small benchmark a couple of years ago and found almost no difference for geometries of few small organic molecules from my studies. But in my systems there were only (intramolecular) H-bonds, there was no any dispersion-bonded complexes. At that time the only more-or-less extensive study I found was this one. See specifically the "Geometry Optimization with DFT-D" section at pp. 564-567. $\endgroup$
    – Wildcat
    Commented Aug 8, 2016 at 19:16
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    $\begingroup$ I quote from the above mentioned article: "The empirical dispersion correction [...] remarkably improves the intermolecular geometries if at least a TZVP basis set is used. This applies especially to the dispersion-bonded complexes, where the RMS error is reduced up to 25 times [...]" $\endgroup$
    – Wildcat
    Commented Aug 8, 2016 at 19:18
  • $\begingroup$ @Wildcat - I appreciate the comments about intermolecular complexes and geometries. I should have been more specific that I was curious about intramolecular parameters and geometries. I have the sense that should be a bit better, since there are intramolecular hydrogen bonding and dispersion effects too, but haven't found much about it. $\endgroup$
    – Geoff Hutchison
    Commented Aug 8, 2016 at 21:29
  • $\begingroup$ A surface science paper by Dr. Greely discussed the effects of vdw correction in furfural adsorption and hydrogenation. ac.els-cdn.com/S0039602813003518/… $\endgroup$
    – Osman Mamun
    Commented Aug 9, 2016 at 16:35
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    $\begingroup$ @GeoffHutchison I'm not aware of an extensive review, but there are several papers looking at the influence of vdW corrections in peptides. Also don't Truhlar's fitting papers on "weakly bound" complexes include dispersion corrected functionals. $\endgroup$
    – Deathbreath
    Commented Aug 17, 2016 at 13:48

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I am afraid I do not know of a paper specifically discussing the effects of DFT dispersion corrections on intramolecular properties. However, it should be noted that for short-range descriptors (such as bond lengths and bending angles) the dispersion corrections will not influence those as they correspond to distances below the typical distance at which the corrections take place. The various schemes differ in how they work, but typically the corrections (in Grimme's schemes) are damped below a distance of ~6 Å. It is also my experience that such local structural characteristics are not affected by dispersion corrections.

However, you are right that dispersion corrections will influence intramolecular structure at larger scale, and in particular for “soft” or “flexible” long molecules with many conformations. There, it is worth noting that the so-called “dispersion” corrections actually correspond to the lack of accounting in local DFT functionals of middle-to-long range correlation effects. Thus, it is actually expected that the corrections — or nonlocal functionals including dispersion terms — actually perform better for those too.

Unless, like Grimme's 2006 two-body dispersion correction scheme (often called “D2”), the dispersion corrections happen to be often too strong and make intramolecular distance somewhat too small (instead of much too large)!

Edit: Now that I come to think of it, one extreme example of intramolecular system that has been studied in detail w.r.t. dispersion corrections is that of helicenes. It was shown (for example there and there) that dispersion corrections improve the accuracy of computational structures and energies compared to experimental (or high-level computational) data.

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    $\begingroup$ We're finishing up a benchmark of conformer scoring for exactly this reason. Our working assumption is exactly that middle-to-long-range effects (e.g., between conjugated segments or intramolecular hydrogen bonds) are not well treated by existing force fields used heavily in conformer generation, nor previous quantum methods. Thus, using at least dispersion-corrected semiempirical methods is needed. $\endgroup$
    – Geoff Hutchison
    Commented Aug 8, 2016 at 21:51
  • $\begingroup$ @hBy2Py Just remove the last forward-slash and it works. (DOI: 10.1021/jp404252v) $\endgroup$
    – LordStryker
    Commented Mar 6, 2017 at 19:13
  • $\begingroup$ Yes, we've done some helicene work so I'm aware of those papers. $\endgroup$
    – Geoff Hutchison
    Commented Mar 8, 2017 at 21:44
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Disclaimer: These articles are from my old group and myself. But they may serve as a starting point for someone's own investigation, even if one disagrees with our conclusions.

The Grimme group, me included, looked at experimental, back-corrected rotational constants of smallish to medium-sized organic molecules a while back. Our conclusion was that a modern dispersion-correction, i.e. D3(BJ) is beneficial for geometry optimization at virtually non-existent computational cost. The references are: T. Risthaus, M. Steinmetz, S. Grimme, J. Comput Chem., 35, 1509 (2014), M. Steinmetz, S. Grimme, Phys. Chem. Chem. Phys., 15, 16031 (2013).

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    $\begingroup$ With that first link, your anonymity is now toast. ;-) $\endgroup$
    – hBy2Py
    Commented Mar 6, 2017 at 16:55
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Our group just published a benchmark, considering ~6500 conformer geometries across ~650 molecules. Using high-level DLPNO-CCSD(T) / def2-TZVP energies, we found a huge increase in accuracy (from several metrics) when using dispersion correction at minuscule cost in time.

'Assessing conformer energies using electronic structure and machine learning methods' Int. J. Quantum Chem. 2020

For example, the mean $R^2$ correlation between B3LYP and DLPNO-CCSD(T) energies was 0.706 without dispersion and 0.920 with -D3BJ dispersion correction. Similar effects were seen with other functionals.

Our conclusion is that intramolecular non-bonded interactions are handled better, and as mentioned by F'x reflect medium-to-long range behavior of standard chemical functionals.

tl;dr - use dispersion correction for any density functional calculation. Even on molecular geometries it's generally better.

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